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Micro-grippers find applications in micro-robotics, microsurgery, micro-fluidics, micro-relays, assembling and miniature medical instrumentation. Actuation principle involved may be electrothermal, electrostatic, piezoelectric, shape memory and electromagnetic. It has been found that thermal actuation provides greater displacement at low voltages when compared to other mechanisms. A 3-D electrothermally driven micro-gripper has been designed using COMSOL Multiphysics. Micro-gripper is comprised of two microactuators (hot-and-cold-arm actuator) which operates on the basis of joule heating and thermal expansion. Despite of the recent progress, most available micro-grippers are still suffering of high voltage requirement. The gripper presented here is geometrically optimized to explore the effect of dimension variation on the performance. The total dimensions of the structure are within 705?m×235?m area, including contact pads. Length and Width of hot beam is 600?m and 10?m respectively whereas length and width of the cold beam is 250?m and 75?m respectively with a common thickness of 5?m.The initial opening between the gripping arms is 15?m. Tip displacement is computed by varying the length of the hot beam and gap between the hot and cold beams. The maximum voltage applied is 3V. When the length of the hot beam is varied from 500?m to 700?m, the displacement increases from 7.36?m to 11.08?m with constant gap of 5?m as shown in figure1 and figure4. When gap between the beams is decreased from 15?m to 5?m, the displacement increases from 6.71?m to 9.22?m with constant hot beam length of 600?m as shown in fig.2 and fig.3.The maximum temperature rise in the structure is 654.30C. It has been concluded that the displacement increases by increasing the length of the hot beam and decreasing the gap between the hot beam and cold beam.